The Mixed-Isospin Vector Current Correlator in Chiral Perturbation Theory and QCD Sum Rules

Abstract

The mixed-isospin vector current correlator, $⟨0|T(V_{\mu }^{\rho }{V}_{\nu }^{\omega })|0⟩$ is evaluated using both QCD sum rules and Chiral Perturbation Theory (ChPT) to one-loop order. The sum rule treatment is a modification of previous analyses necessitated by the observation that those analyses produce forms of the correlator that fail to be dominated, near $q^2=0$, by the most nearby singularities. Inclusion of contributions associated with the $\varphi$ meson rectify this problem. The resulting sum rule fit provides evidence for a significant direct $\omega \to \pi \pi$ coupling contribution in $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}$. It is also pointed out that results for the $q^2$-dependence of the correlator cannot be used to provide information about the (off-shell) $q^2$-dependence of the off-diagonal element of the vector meson propagator unless a very specific choice of interpolating fields for the vector mesons is made. The results for the value of the correlator near $q^2=0$ in ChPT are shown to be more than an order of magnitude smaller than those extracted from the sum rule analysis and the reasons why this suggests slow convergence of the chiral series for the correlator given.

29 pages, uses REVTEX and epsfig.sty with 6 uuencoded figures. Entire manuscript available as a ps file at http://www.physics.adelaide.edu.au/theory/home.html . Also available via anonymous ftp at ftp://adelphi.adelaide.edu.au/pub/theory/ADP-95-20.T179.ps

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• Extension of the Chiral Perturbation Theory Meson Lagrangian to Order $P^6$
• Low-Energy Photon-Photon Collisions to Two-Loop Order
• Light Quark Masses from QCD
• Violations of Dashen's Theorem
• The Momentum Dependence of the $\rho -\omega$ Mixing Amplitude in a Hadronic Model
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• The Off Shell $\rho$-$\omega$ Mixing in the QCD Sum Rules
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• The Mixed Vector Current Correlator <0|T(V^3_μV^8_ν)|0> To Two Loops in Chiral Perturbation Theory
• Comparison of Chiral Perturbation Theory and QCD Sum Rule Results for Pseudoscalar Isoscalar-Isovector Mixing
• Modelling the Off-Shell Dependence of ${\pi }^o-\eta$ Mixing with Quark Loops
• Pi- Eta Mixing from QCD Sum Rules

Cited by in corpus (17)

• Rho-omega mixing, vector meson dominance and the pion form-factor
• Pion Loop Contribution to Rho-Omega Mixing and Mass Splitting
• Extracting the rho-omega mixing amplitude from the pion form-factor
• Inverse-Moment Chiral Sum Rules
• Isospin Breaking and the Extraction of $m_s$ from the $\tau$-Decay-Like Vector Current Sum Rule
• Rho-Omega Mixing via QCD Sum Rules with Finite Mesonic Widths
• Two Model-Independent Results for the Momentum Dependence of Rho-Omega Mixing
• The Mixed Vector Current Correlator <0|T(V^3_μV^8_ν)|0> To Two Loops in Chiral Perturbation Theory
• Isospin-Breaking Vector Meson Decay Constants From Continuous Families of Finite Energy Sum Rules
• Isospin Breaking and $\omega$->$\pi \pi$ Decay
• Rho - Omega Splitting and Mixing in Nuclear Matter
• The Okamoto-Nolen-Schiffer anomaly without rho-omega mixing
• Isospin Breaking Effects in the Extraction of Isoscalar and Isovector Spectral Functions From $e^{+}{e}^{-}\to hadrons$
• On extracting the rho-omega mixing amplitude from the pion form-factor
• Vector Meson Dominance and Rho-Omega Mixing
• Study of the electromagnetic Dalitz decay $J/\psi \to e^{+}{e}^{-}{\pi }^0$
• $\rho -\omega$ Mixing in $J/\psi \to VP$ Decays